The present invention relates generally to apparatuses and methods for electromagnetically confining molten metal and more particularly to an apparatus and method for preventing the escape of molten metal through the open end of a vertically extending gap between two horizontally spaced members between which the molten metal is located.
An example of an environment in which the present invention is intended to operate is a system for continuously casting molten metal directly into strip, e.g. steel strip. Such a system typically comprises a pair of horizontally spaced, counter-rotating rolls defining a horizontally disposed, vertically extending gap therebetween for receiving the molten metal. The gap defined by the rolls tapers in a downward direction toward the nip between the rolls. The rolls are cooled, and in turn cool the molten metal as the molten metal descends through the gap, exiting as a solid metal strip at the nip between the rolls.
The gap has an open end adjacent each end of a roll. The molten metal is unconfined by the rolls at each open end of the gap. To prevent molten metal from escaping outwardly through the open end of the gap, a dam must be employed. Mechanical dams or seals have been used for this purpose, but they have disadvantages which are described in Pareg sic! U.S. Pat. No. 4,936,374 and in Lari, et al. U.S. Pat. No. 4,974,661, and the disclosures thereof are incorporated herein by reference.
To overcome the disadvantages inherent in the employment of mechanical dams or seals, efforts have been made to confine the molten metal at the open end of the gap by employing an electromagnet having a magnetic core encircled by an electrically conductive coil and having a pair of spaced magnet poles located adjacent the open end of the gap. The magnet is energized by the flow through the coil of a time-varying current (e.g., alternating current or fluctuating direct current), and the magnet generates a time-varying magnetic field extending across the open end of the gap and between the poles of the magnet. The magnetic field can be either horizontal or vertical, depending upon the disposition of the poles of the magnet. Examples of magnets which produce a horizontal field are described in the aforementioned Pareg sic! U.S. Pat. No. 4,936,374 and in Praeg U.S. Pat. No. 5,251,685. Examples of magnets which produce a vertical magnetic field are described in the aforementioned Lari, et al. U.S. Pat. No. 4,974,661. The disclosures of all of these patents are incorporated herein by reference.
The time-varying magnetic field induces eddy currents in the molten metal adjacent the open end of the gap. The induced eddy currents create their own time-varying magnetic field which, at the open end of the gap, provides a magnetic flux density which is additive to the magnetic flux density provided by the magnetic field from the electromagnet. The resulting repulsive body force is directed toward the molten metal at the open end of the gap. The repulsive body force can be expressed as
f=J.times.B where PA1 f=the repulsive body force at the open end of the gap PA1 J=the peak induced current density in the molten metal PA1 B=the peak magnetic flux density due to (1) the magnetic field from the electromagnetic and (2) the magnetic field from the induced eddy currents. PA1 P=kB.sup.2 /4.mu. where PA1 PL=B.sup.2 /(2.mu..sup.2 .delta.) PA1 P/PL=.delta.k.mu./2 where
Another expedient for magnetically confining molten metal at the open end of a gap between a pair of rolls is to locate, adjacent the open end of the gap, a coil through which a time-varying current flows. This causes the coil to generate a magnetic field which induces eddy currents in the molten metal adjacent the open end of the gap resulting in a repulsive body force similar to that described above in connection with the system employing magnet poles adjacent the gap. Embodiments of a coil-type of magnetic confining dam are described in Gerber, et al. U.S. Pat. No. 5,197,534 and Gerber U.S. Pat. No. 5,279,350, and the disclosures therein are incorporated herein by reference.
Further with respect to the repulsive body force, the integral thereof gives the average repulsive magnetic pressure P which, in the case of the coil-type embodiment of magnetic confining dam, can be expressed as
k=the coupling factor between the coil and the molten metal PA2 .mu.=the magnetic permeability of air (and of the molten metal) PA2 (.delta.) is the skin depth in copper (the material of the coil) PA2 (.mu.) is the magnetic permeability of air (and of copper and the molten steel) and PA2 (k) is the coupling factor between the coil and the molten metal.
B=the peak magnetic flux density (as described above).
The coupling factor is typically less than one. When the molten metal is steel, and the frequency of the time-varying electric current is 3000 Hertz, the coupling factor (k) can have approximate values somewhere between 0.18 and 0.90 depending upon the geometry of the molten metal pool at the open end of the gap. The coupling factor decreases with increased skin depth (i.e. penetration) of the induced eddy currents in the molten metal. Skin depth increases with a reduction in frequency; therefore, a reduction in frequency results in a decrease in the coupling factor (k) which in turn decreases the repulsive body pressure (p).
In order to contain the molten steel, the repulsive body pressure must be at least equal to the pressure urging the molten metal outwardly through the open end of the gap between the rolls. The repulsive body pressure (P) can be increased by increasing the peak magnetic flux density (B) produced by the dam, but an increase in that flux density also increases the power loss in the dam (power dissipated as heat). Average power loss per unit area in the dam (PL) is expressed as follows:
where (.delta.) is the skin depth in copper, the material of which the confining coil is composed and (.mu.) is the magnetic permeability of copper.
From the foregoing equation it is apparent that power loss in the dam can be reduced by increasing the skin depth (.delta.) which can be increased by reducing the frequency of the time-varying current. However as noted above, a reduction in frequency decreases the coupling factor (k) which in turn produces a decrease in the repulsive body pressure (P).
It is desireable to (1) provide a repulsive body pressure sufficiently high to provide containment of the molten metal while (2) reducing the power loss in the dam. In other words, one should provide a relatively high ratio of containment pressure to power loss in the dam. This ratio (P/PL) can be expressed as follows:
For purposes of this discussion, the magnetic permeability (.mu.) of air, copper and the molten steel can be assumed to be the same.